If Pleft( θ right) = left[ {begin{array}{*{20}{c}} 1&{cot θ } { - cot

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3 and 4 .Determinants and Matrices

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If $P\left( \theta \right) = \left[ {\begin{array}{*{20}{c}} 1&{\cot \theta } \\ { - \cot \theta }&1 \end{array}} \right]$ and $PQ$ = $I$, then $\left( {\cos e{c^2}\theta } \right)Q$ (where $I$ is an identity matrix of $2×2$ order)

A

$P\left( \theta \right)$

B

$P\left( { - \theta } \right)$

C

$P\left( {2\theta } \right)$

D

$I$

Solution

$Q = {P^{ – 1}} = \frac{{\left[ {\begin{array}{*{20}{c}}
1&{ – \cot \theta }\\
{\cot \theta }&1
\end{array}} \right]}}{{\cos e{c^2}\theta }}$

$\therefore {\rm{Q}}cose{c^2}\theta = {\rm{P}}( – \theta )$

Standard 12

Mathematics

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(JEE MAIN-2024)